{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Practical Statistics for Data Scientists (Python)\n",
    "# Chapter 7. Unsupervised Learning\n",
    "> (c) 2019 Peter C. Bruce, Andrew Bruce, Peter Gedeck"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import required Python packages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "from pathlib import Path\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "from sklearn import preprocessing\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.cluster import KMeans\n",
    "from sklearn.mixture import GaussianMixture\n",
    "\n",
    "from scipy.cluster.hierarchy import linkage, dendrogram, fcluster\n",
    "from scipy.stats import multivariate_normal\n",
    "\n",
    "import prince\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import cm \n",
    "from matplotlib.colors import from_levels_and_colors\n",
    "import seaborn as sns\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "DATA = Path('.').resolve().parents[1] / 'data'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define paths to data sets. If you don't keep your data in the same directory as the code, adapt the path names."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "SP500_DATA_CSV = DATA / 'sp500_data.csv.gz'\n",
    "SP500_SECTORS_CSV = DATA / 'sp500_sectors.csv'\n",
    "LOAN_DATA_CSV = DATA / 'loan_data.csv.gz'\n",
    "HOUSE_TASKS_CSV = DATA / 'housetasks.csv'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Principal Components Analysis\n",
    "## A simple example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                 XOM       CVX\n",
      "1993-01-29 -0.016991  0.072921\n",
      "1993-02-01  0.016991  0.102089\n",
      "1993-02-02  0.084954  0.029168\n",
      "1993-02-03  0.067964  0.058337\n",
      "1993-02-04  0.034378  0.044272\n"
     ]
    }
   ],
   "source": [
    "sp500_px = pd.read_csv(SP500_DATA_CSV, index_col=0)\n",
    "oil_px = sp500_px[['XOM', 'CVX']]\n",
    "print(oil_px.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        XOM       CVX\n",
      "0 -0.664711 -0.747101\n",
      "1  0.747101 -0.664711\n"
     ]
    }
   ],
   "source": [
    "pcs = PCA(n_components=2)\n",
    "pcs.fit(oil_px)\n",
    "loadings = pd.DataFrame(pcs.components_, columns=oil_px.columns)\n",
    "print(loadings)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def abline(slope, intercept, ax):\n",
    "    \"\"\"Calculate coordinates of a line based on slope and intercept\"\"\"\n",
    "    x_vals = np.array(ax.get_xlim())\n",
    "    return (x_vals, intercept + slope * x_vals)\n",
    "\n",
    "ax = oil_px.plot.scatter(x='XOM', y='CVX', alpha=0.3, figsize=(4, 4))\n",
    "ax.set_xlim(-3, 3)\n",
    "ax.set_ylim(-3, 3)\n",
    "ax.plot(*abline(loadings.loc[0, 'CVX'] / loadings.loc[0, 'XOM'], 0, ax),\n",
    "        '--', color='C1')\n",
    "ax.plot(*abline(loadings.loc[1, 'CVX'] / loadings.loc[1, 'XOM'], 0, ax),\n",
    "        '--', color='C1')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interpreting principal components"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "syms = sorted(['AAPL', 'MSFT', 'CSCO', 'INTC', 'CVX', 'XOM', 'SLB', 'COP',\n",
    "        'JPM', 'WFC', 'USB', 'AXP', 'WMT', 'TGT', 'HD', 'COST'])\n",
    "top_sp = sp500_px.loc[sp500_px.index >= '2011-01-01', syms]\n",
    "\n",
    "sp_pca = PCA()\n",
    "sp_pca.fit(top_sp)\n",
    "\n",
    "explained_variance = pd.DataFrame(sp_pca.explained_variance_)\n",
    "ax = explained_variance.head(10).plot.bar(legend=False, figsize=(4, 4))\n",
    "ax.set_xlabel('Component')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "       AAPL       AXP       COP      COST      CSCO       CVX        HD  \\\n",
      "0 -0.300825 -0.246332 -0.261529 -0.273634 -0.064059 -0.444490 -0.207983   \n",
      "1 -0.505116 -0.139426  0.174212 -0.416307 -0.031939  0.289373 -0.278002   \n",
      "2 -0.786730  0.135458 -0.002367  0.465862 -0.007524  0.082374  0.166320   \n",
      "3 -0.120586  0.061814 -0.206026  0.092596  0.003904 -0.577665  0.162814   \n",
      "4  0.111576 -0.596666 -0.005813  0.555529 -0.039860  0.109016 -0.185488   \n",
      "\n",
      "       INTC       JPM      MSFT       SLB       TGT       USB       WFC  \\\n",
      "0 -0.076956 -0.196397 -0.105012 -0.481786 -0.148833 -0.116421 -0.145684   \n",
      "1 -0.033898 -0.040723 -0.053954  0.472494 -0.228123 -0.054796 -0.047427   \n",
      "2 -0.003518  0.062261  0.016248 -0.194822  0.160833  0.048976  0.041932   \n",
      "3 -0.001605  0.057687 -0.012558  0.680914  0.109895  0.016752  0.018614   \n",
      "4 -0.072047 -0.385160 -0.077135  0.181332 -0.055557 -0.155440 -0.216425   \n",
      "\n",
      "        WMT       XOM  \n",
      "0 -0.122304 -0.317952  \n",
      "1 -0.222889  0.154192  \n",
      "2  0.175806  0.090167  \n",
      "3  0.058439 -0.295204  \n",
      "4  0.091541  0.013277  \n"
     ]
    }
   ],
   "source": [
    "loadings = pd.DataFrame(sp_pca.components_[0:5, :], \n",
    "                        columns=top_sp.columns)\n",
    "print(loadings)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 5 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "maxPC = 1.01 * np.max(np.max(np.abs(loadings.loc[0:5, :])))\n",
    "\n",
    "f, axes = plt.subplots(5, 1, figsize=(5, 5), sharex=True)\n",
    "\n",
    "for i, ax in enumerate(axes):\n",
    "    pc_loadings = loadings.loc[i, :]\n",
    "    colors = ['C0' if l > 0 else 'C1' for l in pc_loadings]\n",
    "    ax.axhline(color='#888888')\n",
    "    pc_loadings.plot.bar(ax=ax, color=colors)\n",
    "    ax.set_ylabel(f'PC{i+1}')\n",
    "    ax.set_ylim(-maxPC, maxPC)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Correspondence analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "housetasks = pd.read_csv(HOUSE_TASKS_CSV, index_col=0)\n",
    "\n",
    "ca = prince.CA(n_components=2)\n",
    "ca = ca.fit(housetasks)\n",
    "\n",
    "ca.plot_coordinates(housetasks, figsize=(6, 6))\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# K-Means Clustering\n",
    "## A Simple Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                 XOM       CVX  cluster\n",
      "2011-01-03  0.736805  0.240681        3\n",
      "2011-01-04  0.168668 -0.584516        0\n",
      "2011-01-05  0.026631  0.446985        3\n",
      "2011-01-06  0.248558 -0.919751        0\n",
      "2011-01-07  0.337329  0.180511        3\n"
     ]
    }
   ],
   "source": [
    "df = sp500_px.loc[sp500_px.index >= '2011-01-01', ['XOM', 'CVX']]\n",
    "kmeans = KMeans(n_clusters=4).fit(df)\n",
    "df['cluster'] = kmeans.labels_\n",
    "print(df.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        XOM       CVX\n",
      "0 -0.327313 -0.563098\n",
      "1  0.962633  1.379702\n",
      "2 -1.133502 -1.741985\n",
      "3  0.243415  0.337513\n"
     ]
    }
   ],
   "source": [
    "centers = pd.DataFrame(kmeans.cluster_centers_, columns=['XOM', 'CVX'])\n",
    "print(centers)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(4, 4))\n",
    "ax = sns.scatterplot(x='XOM', y='CVX', hue='cluster', style='cluster', \n",
    "                     ax=ax, data=df)\n",
    "ax.set_xlim(-3, 3)\n",
    "ax.set_ylim(-3, 3)\n",
    "centers.plot.scatter(x='XOM', y='CVX', ax=ax, s=50, color='black')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## K-Means Algorithm\n",
    "The _scikit-learn_ algorithm is repeated 10 times by default (`n_init`), `max_iter` is used to control the number of iterations. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "syms = sorted(['AAPL', 'MSFT', 'CSCO', 'INTC', 'CVX', 'XOM', 'SLB', 'COP', \n",
    "               'JPM', 'WFC', 'USB', 'AXP', 'WMT', 'TGT', 'HD', 'COST'])\n",
    "top_sp = sp500_px.loc[sp500_px.index >= '2011-01-01', syms]\n",
    "kmeans = KMeans(n_clusters=5).fit(top_sp)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interpreting the Clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Counter({4: 301, 2: 290, 3: 250, 0: 187, 1: 103})\n"
     ]
    }
   ],
   "source": [
    "from collections import Counter\n",
    "print(Counter(kmeans.labels_))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x432 with 5 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "centers = pd.DataFrame(kmeans.cluster_centers_, columns=syms)\n",
    "\n",
    "f, axes = plt.subplots(5, 1, figsize=(5, 6), sharex=True)\n",
    "for i, ax in enumerate(axes):\n",
    "    center = centers.loc[i, :]\n",
    "    maxPC = 1.01 * np.max(np.max(np.abs(center)))\n",
    "    colors = ['C0' if l > 0 else 'C1' for l in center]\n",
    "    ax.axhline(color='#888888')\n",
    "    center.plot.bar(ax=ax, color=colors)\n",
    "    ax.set_ylabel(f'Cluster {i + 1}')\n",
    "    ax.set_ylim(-maxPC, maxPC)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Selecting the Number of Clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "inertia = []\n",
    "for n_clusters in range(2, 14):\n",
    "    kmeans = KMeans(n_clusters=n_clusters, random_state=0).fit(top_sp)\n",
    "    inertia.append(kmeans.inertia_ / n_clusters)\n",
    "inertias = pd.DataFrame({'n_clusters': range(2, 14), 'inertia': inertia})\n",
    "ax = inertias.plot(x='n_clusters', y='inertia')\n",
    "plt.xlabel('Number of clusters(k)')\n",
    "plt.ylabel('Average Within-Cluster Squared Distances')\n",
    "plt.ylim((0, 1.1 * inertias.inertia.max()))\n",
    "ax.legend().set_visible(False)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hierarchical Clustering\n",
    "## A Simple Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(17, 4)\n"
     ]
    }
   ],
   "source": [
    "syms1 = ['AAPL', 'AMZN', 'AXP', 'COP', 'COST', 'CSCO', 'CVX', 'GOOGL', 'HD', \n",
    "         'INTC', 'JPM', 'MSFT', 'SLB', 'TGT', 'USB', 'WFC', 'WMT', 'XOM']\n",
    "df = sp500_px.loc[sp500_px.index >= '2011-01-01', syms1].transpose()\n",
    "\n",
    "Z = linkage(df, method='complete')\n",
    "print(Z.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Dendrogram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(5, 5))\n",
    "\n",
    "dendrogram(Z, labels=df.index, color_threshold=0)\n",
    "plt.xticks(rotation=90)\n",
    "ax.set_ylabel('distance')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 : COP, CVX, SLB, XOM\n",
      "2 : AAPL, AXP, COST, CSCO, HD, INTC, JPM, MSFT, TGT, USB, WFC, WMT\n",
      "3 : AMZN\n",
      "4 : GOOGL\n"
     ]
    }
   ],
   "source": [
    "memb = fcluster(Z, 4, criterion='maxclust')\n",
    "memb = pd.Series(memb, index=df.index)\n",
    "for key, item in memb.groupby(memb):\n",
    "    print(f\"{key} : {', '.join(item.index)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Measures of Dissimilarity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = sp500_px.loc[sp500_px.index >= '2011-01-01', ['XOM', 'CVX']]\n",
    "fig, axes = plt.subplots(nrows=2, ncols=2, figsize=(5, 5))\n",
    "for i, method in enumerate(['single', 'average', 'complete', 'ward']):\n",
    "    ax = axes[i // 2, i % 2]\n",
    "    Z = linkage(df, method=method)\n",
    "    colors = [f'C{c+1}' for c in fcluster(Z, 4, criterion='maxclust')]\n",
    "    ax = sns.scatterplot(x='XOM', y='CVX', hue=colors, style=colors,\n",
    "                         size=0.5, ax=ax, data=df, legend=False)\n",
    "\n",
    "    ax.set_xlim(-3, 3)\n",
    "    ax.set_ylim(-3, 3)\n",
    "    ax.set_title(method)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Model based clustering\n",
    "## Multivariate Normal Distribution\n",
    "> Define a colormap that corresponds to the probability levels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean = [0.5, -0.5]\n",
    "cov = [[1, 1], [1, 2]]\n",
    "probability = [.5, .75, .95, .99]\n",
    "def probLevel(p):\n",
    "    D = 1\n",
    "    return (1 - p) / (2 * math.pi * D)\n",
    "levels = [probLevel(p) for p in probability]\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(5, 5))\n",
    "\n",
    "x, y = np.mgrid[-2.8:3.8:.01, -5:4:.01]\n",
    "pos = np.empty(x.shape + (2,))\n",
    "pos[:, :, 0] = x; pos[:, :, 1] = y\n",
    "rv = multivariate_normal(mean, cov)\n",
    "\n",
    "\n",
    "CS = ax.contourf(x, y, rv.pdf(pos), cmap=cm.GnBu, levels=50)\n",
    "ax.contour(CS, levels=levels, colors=['black'])\n",
    "ax.plot(*mean, color='black', marker='o')\n",
    "\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mixtures of Normals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4589.259972552867\n"
     ]
    }
   ],
   "source": [
    "df = sp500_px.loc[sp500_px.index >= '2011-01-01', ['XOM', 'CVX']]\n",
    "mclust = GaussianMixture(n_components=2).fit(df)\n",
    "print(mclust.bic(df))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(4, 4))\n",
    "colors = [f'C{c}' for c in mclust.predict(df)]\n",
    "df.plot.scatter(x='XOM', y='CVX', c=colors, alpha=0.5, ax=ax)\n",
    "ax.set_xlim(-3, 3)\n",
    "ax.set_ylim(-3, 3)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean\n",
      "[[-0.0507743  -0.21582045]\n",
      " [ 0.07074619  0.10201778]]\n",
      "Covariances\n",
      "[[[0.98833257 0.99520038]\n",
      "  [0.99520038 1.69955939]]\n",
      "\n",
      " [[0.2710052  0.27825521]\n",
      "  [0.27825521 0.52175755]]]\n"
     ]
    }
   ],
   "source": [
    "print('Mean')\n",
    "print(mclust.means_)\n",
    "print('Covariances')\n",
    "print(mclust.covariances_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Selecting the number of clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAARgAAAEYCAYAAACHjumMAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy86wFpkAAAACXBIWXMAAAsTAAALEwEAmpwYAAA9DElEQVR4nO3dd1xVR/r48c/DpUmvigqIDRsqIvYWjdH0sunFmGqKaZuNKZt8N2422V92k82mN2OKm2aaaRqjiUaNHXsHCyqi0hQBpd75/TGHFhtIOXiZ9+vFi3vmnHvucxAeZ+bMmRGlFIZhGA3Bze4ADMNwXSbBGIbRYEyCMQyjwZgEYxhGgzEJxjCMBuNudwCnEhYWpmJiYuwOwzCM01i1alWWUir8j+VNOsHExMSQlJRkdxiGYZyGiOw+UblpIhmG0WBMgjEMo8GYBGMYRoNp0n0whlGfSkpKSEtLo7Cw0O5Qzlre3t5ERkbi4eFRo+NNgjGajbS0NPz9/YmJiUFE7A7nrKOUIjs7m7S0NNq3b1+j95gmktFsFBYWEhoaapLLGRIRQkNDa1UDNAnGaFZMcqmb2v78TIIxDKPBuE6COXbI7ggM47ReffVVunXrxo033njSY/z8/ABITU0lLi6usUJrEK6RYNZ9Di92gdw0uyMxjFN68803mTt3Lp988ondoTQK10gw0YPAWQIrptgdiWGc1N13383OnTu54IILCAwM5MUXX6zYFxcXR2pqqn3BNRDXuE0d3A66XgyrPoQRj4Gnj90RGU3c33/YxOb0I/V6zu5tAnj6kh4n3f/2228ze/Zs5s+fz+uvv16vn91UuUYNBmDgPVB4GNZ/bnckhmFYXKMGA7qZ1Lo3rJwKibfZHY3RxJ2qptEY3N3dcTqdFduuOrrYdRKMCFzyKvi1tDsSwzitmJgYfvzxRwBWr17Nrl27bI6oYbhOEwmgTTwEtLE7CsM4rSuvvJKcnBx69OjB66+/TmxsrN0hNQjXqcGUy0qBWY/ABS9AuGv+oxlnr6p3iubMmXPCY/Lz8wFdy9m4cWNjhNVgXKsGA+AdBLuXwIp37I7EMJo910swfuHQ8xpY+6kZ3WsYNnO9BAMw8G4oOQqrp9kdiWE0a66ZYCJ6QswwPbK3rNTuaAyj2XK9Tt5yw/4CBzeCsxQcrnuZhtGUue5fXseR+sswDNu4ZhOpXGkxrP0MDm6yOxLD4PDhw7z55psApKenc9VVV9Xq/bfccgtfffVVQ4TWYFw8wRzTY2IWv2p3JIZRLcG0adPmrEsWZ8K1E4x3IPS5CTZ+DXkH7I7GaOYef/xxduzYQXx8PFdffXXFZFJlZWVMmjSJfv360atXL955R4/hUkpx33330aVLF0aPHk1GRoad4Z8Rl0gwpWVO5m87yQ+//wTd0btyauMGZTR9H1wEa6yJn8pK9Pa66Xq7+Kje3vi13i7M1dubv9fbBdl6e9tPejvv4Gk/7vnnn6djx46sXbuWF154oaJ86tSpBAYGsnLlSlauXMmUKVPYtWsXM2bMYNu2bWzevJlp06axZMmS+rryRuMSCebr1Wnc+sFKlu3MPn5naEeIPR+S3ocS13xi1Ti7zZkzh2nTphEfH8+AAQPIzs4mJSWFhQsXcv311+NwOGjTpg2jRo2yO9Raq9FdJBFJBfKAMqBUKZVold8PTLTKZyqlHrXKnwBut8ofUEr9bJWfD7wCOID3lFLP18dFXBbflhd+Tua1eSkM7BB6/AED74Gf98KRfTrhGAbArTMrXzs8qm97+lTf9g6svu0bWn3bv9UZh6GU4rXXXmPs2LHVymfNmnXG52wqalODGamUiq+SXEYClwG9lVI9gBet8u7AdUAP4HzgTRFxiIgDeAO4AOgOXG8dW2feHg7uGt6BxduzWbU75/gD2g+Hu383ycWwlb+/P3l5eceVjx07lrfeeouSkhIAkpOTKSgoYPjw4UyfPp2ysjL279/P/PnzGzvkOqvLOJh7gOeVUkUASqnyTpDLgM+t8l0ish3ob+3brpTaCSAin1vHbq5DDBVuHBjNWwt28Oqv2/notv7Vd5av5VKYq7+CouvjIw2jVkJDQxkyZAhxcXF069atovyOO+4gNTWVhIQElFKEh4fz7bffcsUVVzBv3jy6d+9OdHQ0gwYNsjH6M1PTBKOAOSKigHeUUu8CscAwEXkOKAQeUUqtBNoCy6q8N80qA9j7h/IBf/wgEZkATACIjq55IvDxdOeOYe359+xtrNt7mN5RQdUPcDrhneHQsjtc/1mNz2sY9enTTz89rszNzY1//vOf/POf/zxu39k+d29Nm0hDlVIJ6ObNRBEZjk5OIcBAYBLwhdTDsnlKqXeVUolKqcTw8PBavffmQTEE+Xjw2ryU43e6uUHPq3Wvf87OuoZpGEYN1CjBKKX2Wd8zgBnoJk8a8I3SVgBOIAzYB0RVeXukVXay8nrj5+XObUPa88uWDDal5x5/QOLt4OaA5e/W58cahnESp00wIuIrIv7lr4ExwEbgW2CkVR4LeAJZwPfAdSLiJSLtgc7ACmAl0FlE2ouIJ7oj+Pv6vqDxg2Pw93bn9Xnbj98Z0Bp6/AnWfAyF9btkhWEYx6tJH0wrYIbV+nEHPlVKzbaSxPsishEoBsYrpRSwSUS+QHfelgITlVJlACJyH/Az+jb1+0qpen9IKLCFB4+O7YK3h+PEBwy8BzZ8Adt/gbg/1ffHG4ZRheic0DQlJiaqpKSk+j9x1nYI61T/5zWatC1btlS7e2OcmRP9HEVkVfkQlqpcYiTviRwrLuO9RTvZnpF//M7y5FJlXRrDMOqfy84Hc7S4lP/MSaao1Emnlieorcz5Pz2Nw7hvGj84w7BMnjwZPz8/jhw5wvDhwxk9erTdIdUrl00woX5e/PKXEbQNanHiA3zDYMevcGCDnmLTMGz0zDPP2B1Cg3DZJhJQkVzyCkuO35lwM3j4wLK3Gzkqo7l77rnniI2NZejQoWzbtg2oPpnUM888Q79+/YiLi2PChAmU95OuXLmSXr16ER8fz6RJkyqme2jKXLYGU27m+v1M+modPz80nKgQn8odLYKh9/X6lvXoyXq5E6NZufadpac95txuLZkwvGPF8Vf1jeTqxChyCoq55+NV1Y6dftfph/KvWrWKzz//nLVr11JaWkpCQgJ9+/atdsx9993H3/72NwDGjRvHjz/+yCWXXMKtt97KlClTGDRoEI8//nhNL9NWLl2DAejbLpjSMsVbC3Ycv3PA3VBWBKs+aPzAjGZp0aJFXHHFFfj4+BAQEMCll1563DHz589nwIAB9OzZk3nz5rFp0yYOHz5MXl5exfNIN9xwQ2OHfkZcvgYTEejN1YmRfJG0l/tGdqJN1T6Z8Fi4+GXoePbNs2HUXU1qHCc7PsTXs9bvr4nCwkLuvfdekpKSiIqKYvLkyRQWnr3zGLl8DQbgnnM6ohS8c6JaTOKtENyu8YMymqXhw4fz7bffcuzYMfLy8vjhhx+q7S9PJmFhYeTn51f0ywQFBeHv78/y5csB+Pzzzxs38DPULBJMZLAPVyZE8tnKvWQcOcH/BnuWwU+PQxMedGi4hoSEBK699lp69+7NBRdcQL9+/artDwoK4s477yQuLo6xY8dW2z916lTuvPNO4uPjKSgoIDAwsLHDr7VmM5J3d3YBo/6zgFsGx/B/F/9hnquVU2Hmw3DbzxA9sF4+z2h6zvaRvPn5+fj5+QF6ft/9+/fzyiuvNHocZiTvCbQL9eWy+DZ8snw3WflF1Xf2vk5PibjsTXuCM4wamDlzJvHx8cTFxbFo0SKeeuopu0M6rWaTYAAmjuxEUamTKYv+MB+Mpy/0vQW2/ACH99gSm2GczrXXXsvatWvZuHEjM2fOpLbzJdmhWSWYjuF+XNa7DblHTzDwrt+dgMCKKY0el2G4Kpe/Tf1HL10Tj5vbCSbeC4qC/ndCYGTjB2UYLqrZJZjy5LLtQB4Rgd4EtvCo3HnBv2yKyjBcU7NqIpVLO3SUC15ZyEdLUo/fWVai+2LMVA6GUWfNMsFEBvvw0jXxjBt4ggF2W76H6TfpJ60Nw0ZVH4A8UxdeeCGHDx+u9fs+/PBD7rvvvjp9NjTTBANweZ+2BPt6Hr+j6yXgF2FuWRtnNaUUTqeTWbNmERQUZFsczTbBAKzancO4qcspKCqtLHT3hP53wI55kLHVvuAMl1RQUMBFF11E7969iYuLY/r06cTExPDoo4/Ss2dP+vfvz/btlRPWL1y4kMGDB9OhQ4dqtZkXXniBfv360atXL55++mkAUlNT6dKlCzfffDNxcXHs3buXmJgYsrKyAJg2bRq9evWid+/ejBs3DoAffviBAQMG0KdPH0aPHs3Bgwfr9XqbXSdvVSLCopQsPl62m7tGVFlWtu+tsPBFWP42XPKybfEZDeyDi44v63G5vptYfBQ+ufr4/fE3QJ8boSAbvri5+r6qa1WfxOzZs2nTpg0zZ+pjc3NzeeyxxwgMDGTDhg1MmzaNhx56iB9//BGA/fv38/vvv7N161YuvfRSrrrqKubMmUNKSgorVqxAKcWll17KwoULiY6OJiUlhY8++oiBA6uPSN+0aRPPPvssS5YsISwsjJwcvcTy0KFDWbZsGSLCe++9x7///W/+85//nP5nV0PNugaTEB3MsM5hTFm0k2PFZZU7fMP0Im3pa0xnr1Gvevbsydy5c3nsscdYtGhRxfNE119/fcX3pUsr56m5/PLLcXNzo3v37hW1izlz5jBnzhz69OlDQkICW7duJSVFLzbYrl2745ILwLx587j66qsJCwsDICQkBIC0tDTGjh1Lz549eeGFF9i0qX4X+mjWNRiA+0d15pp3lvLZij3cNrR95Y7zn9cjfOu+WKXRVJ2qxuHpc+r9vqE1qrH8UWxsLKtXr2bWrFk89dRTnHvuuYCuTZer+trLy6vidflzg0opnnjiCe66665q505NTcXX17dW8dx///08/PDDXHrppfz2229Mnjy5tpd0Ss26BgPQv30IA9qH8PaCHRSWVKnFePnp5FKUr29dG0Y9SE9Px8fHh5tuuolJkyaxevVqAKZPn17x/XSL3I8dO5b333+f/Hy9Ysa+ffvIyMg45XtGjRrFl19+SXZ2NkBFEyk3N5e2bfXS8R999NGZX9hJNPsaDMCD53bmhveW82XSXsYNiqnckZkM742GS/4LcVfaFp/hOjZs2MCkSZNwc3PDw8ODt956i6uuuopDhw7Rq1cvvLy8+Oyzz055jjFjxrBly5aKROTn58fHH3+Mw3GSxQaBHj168OSTTzJixAgcDgd9+vThww8/ZPLkyVx99dUEBwczatQodu3aVa/X22ymazgVpRRXvb2U/YeP8dukkXi6WxU7pxNe7ws+oXDHLw0eh9Gwmup0DTExMSQlJVX0jzR1ZrqGWhIRHji3M+m5hXy9Oq1yh5ubnrc3bSWkNXyiMwxXYxKMZXjnMHpHBvLVqrTqO+JvAK8AWPaWPYEZLi81NfWsqb3UlumDsYgIr9+QQLi/V/UdXv7QZxyseAfynzfLm5zllFLV7tIYtVPbLhVTg6kiKsQHbw8HJWVOypxVfpCDJsLtc0xyOct5e3uTnZ1d6z8SQ1NKkZ2djbe3d43fU6MajIikAnlAGVBatTNHRP4CvAiEK6WyRP/38ApwIXAUuEUptdo6djxQPs/fs0qp+r8vVkdph45y3bvLmDS2C5fF69t3BLbVX8ZZLTIykrS0NDIzM+0O5azl7e1NZGTN50yqTRNppFIqq2qBiEQBY4Cq80xeAHS2vgYAbwEDRCQEeBpIBBSwSkS+V0odqkUMDa5NYAv6x4TQ0v8PWbr4KMyaBDFDIf56e4Iz6sTDw4P27duf/kCj3tS1ifRf4FF0wih3GTBNacuAIBFpDYwF5iqlcqykMhc4v46fX+/c3ISXro1nUMfQ6js8WsD+dbDkVbO8iWHUUE0TjALmiMgqEZkAICKXAfuUUuv+cGxbYG+V7TSr7GTl1YjIBBFJEpEkO6uyOQXFvLdoJ87yvhgRGHgPZGyGXQtsi8swziY1TTBDlVIJ6ObPRBEZDvwV+Ft9B6SUelcplaiUSrRz1vQFyRk8O3MLc7dUeXw97krwCTO3rA2jhmqUYJRS+6zvGcAMYATQHlhndQBHAqtFJALYB0RVeXukVXay8ibpkl5taBfqw6u/plTedfDwhn63Q/LPkH2CZWgNw6jmtAlGRHxFxL/8NbpTd6VSqqVSKkYpFYNu7iQopQ4A3wM3izYQyFVK7Qd+BsaISLCIBFvn+blhLqvu3B1uTBzZiU3pR5i/rcqDZIm3w4C7dJ+MYRinVJMaTCvgdxFZB6wAZiqlZp/i+FnATmA7MAW4F0AplQP8A1hpfT1jlTVZV/RpS2RwC179dXtlLca/lV59IKCNvcEZxlngtLeplVI7gd6nOSamymsFTDzJce8D79cuRPt4ONy455yOPDljI4tSshgeW6VPaNciKMqDrhfaF6BhNHFmJO9pXNU3ktaB3tX7YgDm/xNmPwbOspO/2TCaOZNgTsPL3cHdIzqStPsQS3dmV+4YeI9ex3rbLPuCM4wmziSYGri2XxQt/b147dfK2d7pehEERptb1oZxCuZp6hrw9nDw3BU9qz9p7eaAARNgzlN6cvA2fewL0DCaKFODqaHzurciPiqoemHCzRDSAXKb7HAew7CVSTC1kJ1fxKNfrWPNHuv5TO9AuG8VdLvY3sAMo4kyCaYWvDwcLEzOYtuBvMpCNzcoK4X0tbbFZRhNlemDqQU/L3cWPHoOXu5/mL3917/Diinw54160TbDMABTg6k1L3cHSqnqtZg+46C0EJa/Y19ghtEEmQRzBqav3MvYlxeyZf8RXRAeq29br3hXL9RmGAZgEswZuSCuNX5e7rw+v8q4mCEPQuFhWPM/2+IyjKbGJJgzEOjjwfjB7Zi1YT/bM6ymUlR/iB4Myad6DtQwmheTYM7Q7UM70MLDwevzqtRirvkIbpphX1CG0cSYBHOGQnw9uWlgO75fl87OTKvfxa+lvm1dXGDm7TUMTIKpkzuHdcDL3cHLv6RUFh7YCP/tASlz7QvMMJoIk2DqINzfi1uGxPDD+nS2Hii/o9QFPHxh8cu2xmYYTYFJMHV01/AO+Hm68585ybrA4QGD7oXdi2HvSnuDMwybmQRTR0E+njx0XizxUUGVE1IljAfvIFOLMZo986hAPbh96B9WC/Tyg/53wsIX4dBuCG5nT2CGYTOTYOqJ06mYuWE/kcEt6BMdDAPuhk7nmeRiNGsmwdST4jIn//hxMyNiw3WC8Q0zDz4azZ5JMPXE28PBF3cNIirEp7JQKZj1iF4NcuQT9gVnGDYxnbz1KCbMF4ebkFdYojt8ReBoDix7Ewpz7Q7PMBqdSTD1bNuBPIb+az5zNltrWg95EIqOwKoPbY3LMOxgEkw96xjuS6ivJy/NSabMqaBNPHQ4B5a+CaVFdodnGI3KJJh65u5w46HzYtl2MI8f16frwiEPQv4BWD/d3uAMo5GZBNMALu7Zmq4R/vx3bjKlZU7oMBJGPgnthtgdmmE0KpNgGoCbm/CXMV1IzT7K16vTdGfviEchtKPdoRlGozIJpoGM7taS3lFBvPrrdopKrfWr962GuX8zUzkYzUaNEoyIpIrIBhFZKyJJVtkLIrJVRNaLyAwRCapy/BMisl1EtonI2Crl51tl20Xk8Xq/miZERHhkTCz7Dh/j8xV7deG+VbD4Fdi9xN7gDKOR1KYGM1IpFa+USrS25wJxSqleQDLwBICIdAeuA3oA5wNviohDRBzAG8AFQHfgeutYlzW0UxgD2ofw+vztHCsug/gbwSdUJxnDaAbOuImklJqjlCq1NpcBkdbry4DPlVJFSqldwHagv/W1XSm1UylVDHxuHeuyRIRHxnYhJtSHrPwi8PTRzyil/AwHN9sdnmE0uJomGAXMEZFVIjLhBPtvA36yXrcF9lbZl2aVnay8GhGZICJJIpKUmZlZw/Carn4xIdUfIeh3B3j4mFqM0SzUNMEMVUoloJs3E0VkePkOEXkSKAU+qY+AlFLvKqUSlVKJ4eHh9XFK24kIGUcKmb81A3xCYPAD5o6S0SzU6GFHpdQ+63uGiMxAN3cWisgtwMXAuapitiX2AVFV3h5plXGKcpf3j5lbWJSSybInzsXbPPhoNBOnrcGIiK+I+Je/BsYAG0XkfOBR4FKl1NEqb/keuE5EvESkPdAZWAGsBDqLSHsR8UR3BH9fv5fTdD06tgvfTRyCt4e1rrXTCVt+1A9DGoaLqkkNphUwQ0TKj/9UKTVbRLYDXsBca98ypdTdSqlNIvIFsBnddJqolCoDEJH7gJ8BB/C+UmpTvV9RE1V1Gocyp8KRlQzTb4SRT8GISTZGZhgNR1QTHvSVmJiokpKS7A6j3jidirs/XkXrQG/+flkcfHK1Hnz3543g0cLu8AzjjInIqipDWCqYkbyNyM1NCPXz5NMVe0g7dBSGPARHs2DNx3aHZhgNwiSYRnb/qM4Iwmu/bod2gyGyHyx9HcpKT/9mwzjLmATTyNoEteDGgdF8tTqNXdlH9VQOSkHuHrtDM4x6ZxKMDe49pxOeDjde/iUZulwE96+GkA52h2UY9c4kGBuULzn7/bp0tmUUgMMdSo5BbprdoRlGvTIJxiaVS85u002kqefBdxPtDssw6pVJMDYJ8vHkzuEdmLP5IOv35ULclbDzN0hfa3dohlFvTIKx0a1DYmgb1IKUg/mQeBt4BZiHIA2XYhKMjfy9Pfht0jlc2TcSvAMh8VbY/C3k7LQ7NMOoFybB2MzD4YZSihW7clAD7gY3d9g0w+6wDKNemATTBPy4fj/XvLOUJRmecM9SGPqw3SEZRr0wa1M3AWN6tOKFq3rRv30IOMJ0YVkJODzsDcww6sjUYJoAL3cHVydG4eGw/jnWfAyv9IaifHsDM4w6MgmmCfl+XTrjpi6nLDQWjuyD1dPsDskw6sQkmCZmUUoWP+a01atALn1DN5UM4yxlEkwTUr7k7Mu/pFA26AE4kgYbv7Y7LMM4YybBNCFubsLD58WyK6uAr450g5bdYfGrZiVI46xl7iI1Med1b6WXnJ23gyuufRFP31C9trVhnIVMDaaJqbrk7Gf720LLrnaHZBhnzCSYJmhopzD6ly85m50GX4yHvSvtDsswas0kmCZIRJg0tguZeUV8uvaQfsp68ct2h2UYtWYSTBPVLyaEEbHh/JZ6FPrfCVtnQmay3WEZRq2YBNOEvXpdH6bd1h/63wXuXrDkVbtDMoxaMQmmCQv08UBEOCSBFPW8AdZPhyP77Q7LMGrMJJgmLvdoCSNemM/7zoth4L26JmMYZwkzDqaJC/Tx4OHzYhnUMQwizrU7HMOoFZNgzgK3DGlfuZE8B4rz9By+htHEmSbSWWLf4WM8+PkaCn9/DWY/AaVFdodkGKdlEsxZ5KcNB/if2xWQfxDWfW53OIZxWjVKMCKSKiIbRGStiCRZZSEiMldEUqzvwVa5iMirIrJdRNaLSEKV84y3jk8RkfENc0muqW1QC24YEM3zya0oCu+pb1k7y+wOyzBOqTY1mJFKqXilVKK1/Tjwq1KqM/CrtQ1wAdDZ+poAvAU6IQFPAwOA/sDT5UnJqJl7R3bE0+HgM48rIHu7HnxnGE1YXZpIlwEfWa8/Ai6vUj5NacuAIBFpDYwF5iqlcpRSh4C5wPl1+Pxmp6W/N+MHx/Dsrs4cC+8Nnj52h2QYp1TTBKOAOSKySkQmWGWtlFLlo74OAK2s122BvVXem2aVnay8GhGZICJJIpKUmZlZw/Caj7tHdKCFpxcP+b0InUbbHY5hnFJNE8xQpVQCuvkzUUSGV92plFLoJFRnSql3lVKJSqnE8PDw+jilSwny8eSOYR34eUsm6/ce0tNqLnnN7rAM44RqlGCUUvus7xnADHQfykGr6YP1PcM6fB8QVeXtkVbZycqNWrptaAzBPh7837cbKdu7Eub+DXYtsjsswzjOaROMiPiKiH/5a2AMsBH4Hii/EzQe+M56/T1ws3U3aSCQazWlfgbGiEiw1bk7xiozasnf24P/96eebD2Yz7o+z0BoJ/jqNsg7YHdohlFNTUbytgJmiJ620R34VCk1W0RWAl+IyO3AbuAa6/hZwIXAduAocCuAUipHRP4BlM+c9IxSKqferqSZOT+uNYseDaZlgDcEToMpo+DLW2H8D+AwA7SNpkFUE55QOjExUSUlJdkdRpM3Y00a/Y78QuT8h2DcDOg40u6QjGZGRFZVGcJSwYzkPcsVFJXyr5+28d+DfWDiCpNcjCbF1KXPcr5e7ky/ayBtg1pA+dKzO+ZBUDsI7WhvcEazZ2owLqBdqC/uDjey8ov4YWUyfH2Hnii85JjdoRnNnEkwLuSN+dt54JsU1vd7Hg5ugFmP2B2S0cyZBONCHh3blS6t/Bm3MIjcfg/Bmo9h9f/sDstoxkyCcSEtPB28fVNfnEoxbsdIymJG6FpMzk67QzOaKZNgXExMmC8vXRPP+vQCnvP+C4x9DoLbn/6NhtEATIJxQed1b8V9Izvx/tp8Pldj9NrWR9KhCY95MlyTSTAu6s/nxTKscxh/+34TWzevgzcGmocijUZnEoyLcrgJr1zXh3A/L27/LovimOHwy2RIXWx3aEYzYhKMCwvx9eStmxK4IiESx+VvQHAMfHUr5B20OzSjmTAJxsX1igzikbFdcLQIpPBPH0HhEfj6digrtTs0oxkwCaaZ2J6Rx4hpB9mUMBkCo8BpEozR8MyzSM1EZLAPiTEhOBJugIi7daFS+g6TYTQQU4NpJrw9HLxxQwJdIwIAKD24FaaeBzm7bI7McGUmwTQzSime+GY9z8/ZicpKhi/HQ0mh3WEZLsokmGZGRGgd2IL3Nil+6/YM7F8HPz1qd1iGizIJphm6b2QnRnVtyYQVLTnQ6x5Y/RGs/dTusAwXZBJMM+TmJvz3mnhaB7bgyi2jKI4aohOMeZTAqGcmwTRTgT4evHVTAlnHyri35CFKr//S3FEy6p1JMM1YjzaB/POKnvySWsIL81LhaA4sfsXUZIx6Y8bBNHNX9o1kzd5DvLNgJ5cWzaLH2mfAzR0GTbQ7NMMFmBqMwf9d3J34qCD+mjYA1fUivVLknmV2h2W4AFODMfByd/DuuL74eLkjzjh49xz48ha4axH4mfXBjTNnajAGAC0DvPHzcueYw58fu/0LdewQzH7c7rCMs5ypwRjVfLd2H0/ML6XrxW/RqdcQu8MxznImwRjVXNsvim6tA+gUFaQLykohZweEd7E1LqNhFZWWkXIwn837j7DF+opt5c8zl8XV6bwmwRjViAi9reSyZEcW8eufw2fbN3DXQghuZ29wRr3IzCuqSCL6K4/tmfmUOfXwBG8PN7pEBBDm51XnzzIJxjih3KMl3DVtFSPChvCa+hL5cjzc9jO41/2XzmgcpWVOdmYVsDldJ5LNVjLJyi+qOKZ1oDfdWgcwuntLurUOoFvrAGJCfXG41c+gyxonGBFxAEnAPqXUxSJyLvACuqM4H7hFKbVdRLyAaUBfIBu4VimVap3jCeB2oAx4QCn1c71chVHvAn08ePaKOB78fC1De/yV63Y8AbOfgItfsjs04wRyj5ZUa95sOXCE5IP5FJc6AfB0uNGppR8jYsPp1tqf7m0C6BYRQLCvZ4PGVZsazIPAFiDA2n4LuEwptUVE7gWeAm5BJ5BDSqlOInId8C/gWhHpDlwH9ADaAL+ISKxSqqx+LsWob5fFt2Xt3sM8vhgSe95Gp6SpED0Qel1jd2jNltOp2J1z9Lgmzr7DleuQh/p60r1NALcMjqFba3+6tQ6gY7gfHo7Gv2lcowQjIpHARcBzwMNWsaIy2QQC6dbry4DJ1uuvgNdFRKzyz5VSRcAuEdkO9AeW1vEajAb01wu7sSEtl8u3jmZJt8MEhHayO6Rmo6TMyYZ9uWxOP1JRO9l2II+jxfr/ZIeb0CHMl77tgrlpYDtdM2kdQLi/F3KGz5UVlpSxPSOf9MPHGNMjos7XUNMazMvAo4B/lbI7gFkicgw4Agy0ytsCewGUUqUikguEWuVVh4emWWXViMgEYAJAdHR0Ta/DaCAeDjfevDGBC1/9ncvTx/NtaE8CCo/A5m+h26XQIsjuEF2G06nYvP8IS3ZksXh7NitTcyqSib+3O91bB3BNYhTdrb6Szq388PZw1Okzi0udvPXbDrYdPMLWA3mkZhXgVLpJtemZsXWu9Zw2wYjIxUCGUmqViJxTZdefgQuVUstFZBLwEjrp1IlS6l3gXYDExETz1F0T0DLAmzdu6MMN7y3nkS/W8U7CHuT7+2HmI9DlAuh1LXQaDe4N2553NUopdmQWsGRHFku2Z7NsVzaHj5YA0KmlH1f1jWRQh1B6RgbSNqjFGdVKlFJk5hWRXVBMt9a6wXHbhytpHejNc1f0xMMhvL94F8E+HnSJ8Ofinq3pEhFAlwh/HPXwdH1NajBDgEtF5ELAGwgQkZlAV6XUcuuY6cBs6/U+IApIExF3dPMpu0p5uUirzDgLDOgQyhMXdOXZmVt4O6oX99w5D9ZNh41f69pMixCYuMI8WnAaaYeOsmRHNkt3ZLNkRxYHj+g7Om2DWnBet1YM6RTGoI6htArwrvW584tK2XYgz/o6wraD+vWhoyV0CPdl3l/OAaBLhH/FLWgRYcWT5+LlXrea0MmcNsEopZ4AnrCCOQd4BLgcOGB10iYD56E7gAG+B8aj+1auAuYppZSIfA98KiIvoTt5OwMr6vNijIZ1+9D2pGYX0DMyCNp2YlVpB1b73Ma48J14py+rTC6/TAZ3b90ZHNLBzpBtl5VfVJFMluzIZnf2UQDC/DwZ1DGMwR1DGdIxjKiQmtdQSsqcpB06RvswXwBempvMN6vTSDtU2dHr4+kgtpU/Y3tE0CXCv6L2AvDY+V2rna+hkguc4TgYq2/lTuBrEXECh4DbrN1Tgf9Znbg56DtHKKU2icgXwGagFJho7iCdXUSEZy/vWbH9e0oWby3Yxc1Pj4UeF/JF0l5y8ou4fs8GAvb8ivz2/yCyP/S+Fnr8CXxCbIz+zBWXOjl0tBh/b3d8PN0pKXOSU1BMYAsPvD0cFJaUcehoMQB5haWs2XOYVbtzSEo9xM6sAgB8PR30bx/KLYNj6NsumDA/T8L8vPF0d6OgqJT03BNPvF5c6mRnZj5bD+QxfnAMfl7uvPprCm/+toPNz4zFy92Bn5eDPtHBXNcvii4RAXSN8KdtUAvc6mksS12IasKTCyUmJqqkpCS7wzBOIfdoCYE+HgBM/HQ1M9fvB6CD52HuClnN6JL5hBbsoGzQAzjG/gOcZVBWAh61bwI0NKUUB44UsvVAHlv362bG1gN57MjMp6RM8Y/L4xg3sB0b9+Vy8Wu/8+64vgyPDWfKwp38Z27yac//7ri+jOkRwbytB7ntwyS+mziE3lFBfL5iD49/s+G07y8/fnP6EVIy8hjbI6LOnbz1RURWKaUSjys3CcaoT5l5RazYlcOyndks35VN8sE8uskeij0CaNOuM7dF7GLk+kehx+W6czh6ELg1/viMgqJSikqdhPh6kplXxH2frmbrgTxyj5VUHNMm0JuurXWHZ9ugFgxoH0JMmC+/p2TyyfI9ZOUXsTk9j+IyJ24CUcE+dGzpS6eW/kSHtMD9D9c1tHMYkcE+7Dt8jEXJmZzXvRWhfl7syMxnVeqhE8bp5ia0D/Ohcyt/Arw9GvRnUhcmwRi2yM6vTDjLduZwYctsHvT5GbX5e6SkgGM+bWnR9zoY9hfw9K33zy9zKnZnF7DtQB4ON2FMjwiUUvScPIer+kYy+dIelJQ5uWHKMjq38qdrhD9dIwLo0sqfQB8PypyKLfuPVPSjrNiVQ0FxGSLQvXUAgzuGMrhTGP1iQvDzar5P3pgEYzQJZU6Fw03IzMnhg/de52bf5UQU72bHDYt56rstXBG6m45de9MjtnOtq/85BcVs3a+bNVut5k3ywTwKS/Rw+fioIL6dqKegmL5yDx3C/egXU71fqMyp2Jx+xEqI2axIzSGvUK/j3THcl8FWx+zADqENPsz+bGISjNF0lRSyKv0oT3+7gfdyxhNGLotVL9aGjEW6Xkxi5zYkRAdXSzg7M/PZnX2UkV1bAjD+/RUsSM6s2B/q60nX1lZtJMKfbhEnHphWWuZk8/4jFTWslbtyyCvSCaVDmC8DOoQwsEMoA9qHEhHY9PqNGkRZKRQdqVWnvEkwxlkhb89GspZMI2TndwQWHyBfefNs6U18w2ji2gYw/a5BeDjcmPz9Jr5M2suGyWNxcxO+WLmXI4UldLGaOOH+J37qu7TMycb0Iyy3aigrUw+RX55Qwn2tZKKTypmMRWmSykrh0C44mm195ejv0YMgegAc3gNf3V65v/AwePrDX9Nq/BEnSzDNt9FoNEn+0XH4R/8bnM/DniV4rvmMa0KGE1gQw8Edayn56gM82g/g7k49uKlfv4qlnK7pF3XC85WUOdm4L5dlO3NYviubpCoJpWO4L5fFt6lIKi3tTigF2VCcB8Exenvxq6DKYOif9fbsv4LDExLG6SSx9HUI7wrDJ8G8f8Dm7/SKED6hOlEI0P0KGHgPvH7c3z74tYKEm6H/XeDpAwc3QXgsdB6rz6FUndfKMgnGaJrc3CBmKJ4xQ0kAEgDWrYc5v8GWL4kAcHhB615w1QcQFAUlhZSIBxvSK5s8q1J1pyzo4feX99EJpX/7EFr6N3JCOZQK+RkQ1V9vL34FDu+Fi17U21/dCoVH4MJ/w8GNsOEr/QcP8Eq8fj8KFv9XlwXHQEh7cHPAyqmgSnXNI6A1tOoBR7PAOxC8g+BPU2DDl7o88TadQOY+DaGd9ADJm7/TCSyqv77DV09ME8k4uygFuXth3ypIS8KZvoa1w6eydE8BMaufZ/CR2ax1dmCtsxNZgXH4dhhA79gO9G8fctJmU73J3KZrAXF/0ttL34Dk2TD+B7397b2wYx78ZaseDzRrEuQdgOs/hR8fhq0/Qv7ByvN1OEf/4QP88nddm/AJrfwKjoGwzpU/FxtX5jRNJMMlFJcp1h/2Y3lGT5altSEpdRjHtq0G4OaQrkSEHSOxZBvnHPkGOfo17AyFK3foP74d8/T/8BE9z2yg38HNsONXGHA3ODx0rWHBv+HPG/X2hq9g4QvQ7RK97dECvAL0H/+B9bpJ0joepoyCjC3gGw4PrdfndnNAu8G6htEqTn8PrNLsG/30qWNrosv+mgRjNGlKKVIy8lmwLZOFKZmsTM2puO3cNcKfa/tFMbBDCP3bhxLie1HlG4vyIH2tbiaU//H99BhkJYObB0TEQdtE6HSufiIcoLgADmzU+zx9YcuP8OOf4a4FENAG0lbAnKeg+2UQFA1B7SB2DJQc0wmlzzh9zk0zIGOzrtFc+7H+/FUfQtL7+qHQiDjoe4tOJOU1jwtfaMwfa6MxTSSjyck9VsLi7VkVSWW/9ZxO55Z+DOkUVtGHElLbcShH9sO+pIrmFftW6URxzf90U+P9sbB3OYz6G/S5CfLSYcV7cM5j+riifHCW6lpJQabuJ4nqD17+Onn89BiU6WeScPPQKzGMmwF+LSE3TXfA+rVqsrWNujBNJKPJcjoVG/blsiA5k4XJmazZe5gyp8Lf251hncN4KDacYZ3DaRPUonYnLiuFjE261hAUBc4S+PmvcO7TMHoyZCbD20N1rcY3DIrzQdxg3jP6KzAKRj2lk0v2Dt0kOrhR97MczdKfMf4HaD9c10YG3lPZvAntXH1+nMDIevt5nU1MgjFskZlXxKKUTBYkZ7IoJYucgmJEoGfbQO49pyMjYsOJjwrCvSYzqpU3M5xlMP+f0DYBul4EpYXwznAY+SSMeBT8IiCyn65RgK61PLlf938A3LMEio/q/pLyGo5PmN5XeFjXUlp2002q8kTSpo/eH9W/8u6QUcE0kYxGUVLmZPXuQyxI1kllU/oRQM+LMrxzOCO6hDO0Uxihp1uLJ2s7lB7THbUAU8fqW9XlfRgv9YCeV8J5z+jtbT/pZBB04nEyNeZ0AqoyGRnVmCZSfcrYCnuWQuKtenvtp/oOwrhv9PaaTyD5J93BB7DmY0j9Ha54u3L/vlWVS4Cs+QQyt8CYZyvPl7MLRj1ZuZ1/sHLA1brP4dhhGHi33s7P0P0CTWwKhLRDRyuaPYu3Z5NfVIrDTejbLphJY7swIjac7q0Djp+3pLS4snmxYgoU5sLwR/T2N3fosR3lt2/bDa4cmAbw4DpwVPm1Lu/ArSsbnvh2BSbBnIhSulPOP0LfHUieA4tehJu+1h1623+BOU/qSa99Q6G0SLffyxXl6fEN5fIzICulcvtQKqSvqdzO2Ay7l1RupyVB+urKBLNrIWRurUwwW2fqsSDlCeabCfqPcMJ8vb3sLT24Kv56vV31D7YBFZaUsWxnNguTs1iQnMGOTD3ZUtugFlzSuw0jYsMZ3Cm0+rQD+9fruy29rtbb302EvSvgvpV6e+8K3aFanmDOf17/G5T74+1bh/mVbkpMEwl0MtnwJfS8BgLbwsZv9KjKuxfrW4rbf4FF/9U1kKAoPUy7rLjp3BHY9pOOp/tlenvKKN0xefWHevv1frp/4LI39HbS+9Cyu17jqA7KJ60ub/Ys35lNUakTT3c3BnYIZURsOCM6BtDRkYmEd9E/q3Wfw+ppcMtMvf3zk7DyPfhrum5+bPpWPxsz5IHyD2kaP2PjlJp3E8lZpu8CtAjWw6Kzd8CX42H03/U4iPwMPY9seDedYKIGwMX/1QkE9Iz5nUZXnq+pTf34x2bAnfP0rHHl+oyr7INQSg8J73e7TjBKwSu9YcBdMGii3t74NUQmVm96WHIKilmxK6ei6VO+4FeHMB9uGBDNhS1ziD80B49zJoF3ACx9E35+Aibt0HdqxE0/T1Ocr2sig++HQffpcjh+mLpJLmc1l0gwSqnqEyaXFMLv/9V/QB1H6ir2G/3gghdgwASdIPwi9C866A7Dx3ZXrvET2FY/r3E2c1RphpTXBkD/wT66QzfrQH/vcI4eNAa6dvb17TD2/1Ha/26Sd++l5Xc3MMP/Jj493I30rEMMddvANveu9OjUgcm9chi14TEcN34DrXvA1lkw522Iv0b/XDuP0YmlfE3rXtdUXxnSv+6LexlNl0skmJfnJnNN0nU4ul1AxBX/1Ilj6Rv6f8WOI3VN5E9TKm8jtgiGm76qPIHDo3ktIObpWzl7nIc3XPoqoGfAX5taSGqvz1i5VrHopzkEFR/keQ9hTd5ROsX4cU+XfK5Z9R9KrvwIj56JkBMCJRfoVQQAOp8HTx6ovNsS1kl/Gc2SS/TBvDF/OwEL/o+k4hj2R1/KncM7cG7nINw8GvjhtrNYSZmTLfuPsGbPYVbvOcSaPYfZk6OX1HB3E7q3CSAhOpg+0UEkRAcTGWwtq1GYqztlw7vqJpBh0AwmnMovKmX6yr28//su9h0+RocwX24f1p4rEyKbzMzrdso4UsjqPYdZYyWT9fsOVzzT09LfqzKZtAumZ9tA8zMzasXlE0y50jInP208wJRFO1mflkuIryfjBrZj3KB2FavZubriUj0N5OrdhypqJ+WdsR4OoUebwGoJpU2g9xkvlm4Y0IwSTDmlFCt25TBl0U5+2ZKBl7sbf0qI5I5h7ekY7lfPkdprf+4x3dTZfYg1ew+zYV8uxaW6dtI60LsimfSJDqZHmwBTOzHqXbNLMFVtz8hn6u+7+Hp1GsWlTkZ3a8Wdw9rTv33IWfc/t1KKnVkFLEzOJClV11DKnzb2dHejZ9tAEqxk0ic6iNaBtXxA0DDOQLNOMOWy8ov439Ld/G/ZbnIKiukdGcidwztwfo+Imj1UZ5MjhSUs2Z7NwpRMFmyrHHvSNqgFCe2C6ROlmzrdWwfg6d50r8NwXSbBVHGsuIyvV6cx9fdd7MoqoG1QC24f2p5r+kU1icWznE7FxvRcFiZnsjA5i1V7DlHmVPh6OhjcKUyPkI0NJyrEx+5QDQMwCeaEnE7FL1sO8t6iXaxIzcHf250bB7TjlsExjb4GTtXpC35PySK7QE9cFNc2gOGdwxkeG05CdLCpoRhNkkkwp7F272GmLNrJTxv243ATLundhjuHdaBb64YZ61Fc6mTV7kMVzZ7N+yunLxjWOZzhsWEM7RTe8BNVG0Y9qHOCEREHkATsU0pdLLp39FngaqAMeEsp9apV/gpwIXAUuEUptdo6x3jgKeuUzyqlPjrVZ9oxH8zenKNM/X0XXyTt5WhxGcM6h3HnsA4M6xxW5w7h3dm6c3ZBchZLd2RRUFyGu5uQ0C64otlzwukLDKOJq48E8zCQCARYCeZWYCQ6gThFpKVSKkNELgTuRyeYAcArSqkBIhKCTlCJgAJWAX2VUodO9pl2TjiVe7SET1bs5sPFqWTkFdE1wp87hnXg0t5tatxMKSgqZdnO7IoHA1Oz9UjZqJAWepKl2HAGdQzFv+r0BYZxFqpTghGRSOAj4DngYSvBrABuUEpt/8Ox7wC/KaU+s7a3AeeUfyml7jrRcSfSFGa0Ky518v26dKYs3Mm2g3m0CvDilsHtuaF/NIE+1RODUoot+/Mqmj1Ju3MoKVO08HAwqKOevmB4bDgxoT5n3e1xwziVuk7X8DLwKFBlph86AteKyBVAJvCAUioFaAvsrXJcmlV2svI/BjoBmAAQHR1dw/Aajqe7G1f1jeTKhLYsSsliyqKd/Gv2Vl6bl8K1/aK4um8UKRl5LEzOYmFKJpl5+inlrhH+3DakPSNiw+kbE4yXuxncZjQ/p00wInIxkKGUWiUi51TZ5QUUKqUSReRPwPvAsLoGpJR6F3gXdA2mruerLyLCcKsGsjn9CO/9vpOPl+3mg8WpAAT5eOjO2c5hDI8Nd52F0w2jDmpSgxkCXGr1rXgDASLyMboGYk1CywzgA+v1PqDqDMuRVtk+dDOpavlvZxq4nbq3CeCla+J5dGxX5m/LoFvrAHq2DcRhOmcNo5rT9lYqpZ5QSkUqpWKA64B5SqmbgG/RnbwAI4Bk6/X3wM2iDQRylVL7gZ+BMSISLCLBwBir7KwVEejN9f2jiY8KMsnFME6gLsNWnwc+EZE/A/nAHVb5LPQdpO3o29S3AiilckTkH4A1mzPPKKVy6vD5hmE0cWagnWEYdXayu0hm3LlhGA3GJBjDMBqMSTCGYTQYk2AMw2gwJsEYhtFgTIIxDKPBNOnb1CKSCey2O44aCAOy7A6iETW36wVzzafTTikV/sfCJp1gzhYiknSiMQCuqrldL5hrPlOmiWQYRoMxCcYwjAZjEkz9eNfuABpZc7teMNd8RkwfjGEYDcbUYAzDaDAmwRiG0WBMgjlDIhIlIvNFZLOIbBKRB+2OqbGIiENE1ojIj3bH0hhEJEhEvhKRrSKyRUQG2R1TQxKRP1u/0xtF5DMROeP5X02COXOlwF+UUt2BgcBEEeluc0yN5UFgi91BNKJXgNlKqa5Ab1z42kWkLfAAkKiUigMc6Jksz4hJMGdIKbW/fEE5pVQe+pfuuFUSXI21hM1FwHt2x9IYRCQQGA5MBVBKFSulDtsaVMNzB1qIiDvgA6Sf6YlMgqkHIhID9AGW2xxKY3gZvYSN0+Y4Gkt79LI8H1jNwvdExNfuoBqKUmof8CKwB9iPnlN7zpmezySYOhIRP+Br4CGl1BG742lIVZewsTuWRuQOJKCXRu4DFACP2xtSw7Em5L8MnVjbAL4ictOZns8kmDoQEQ90cvlEKfXN6Y53AeVL2KQCnwOjrCVsXFkakKaUKq+dfoVOOK5qNLBLKZWplCpBL000+ExPZhLMGRK99utUYItS6iW742kMp1jCxmUppQ4Ae0Wki1V0LrDZxpAa2h5goIj4WL/j51KHTu26LFvS3A0BxgEbRGStVfZXpdQs+0IyGsj96CV6PIGdWEvxuCKl1HIR+QpYjb5TuoY6PDJgHhUwDKPBmCaSYRgNxiQYwzAajEkwhmE0GJNgDMNoMCbBGIbRYEyCMVyaiJwjImc8UMyoG5NgDFd3DnUYiWrUjUkwzYCIxFjzmEyx5vmYIyItTnJsJxH5RUTWichqEeko2gvW/CAbRORa69hzRGSBiHwnIjtF5HkRuVFEVljHdbSO+1BE3haRJBFJtp5pQkS8ReQD69g1IjLSKr9FRL4RkdkikiIi/64S3xgRWWrF9qX1LBgikioif7fKN4hIV+sh1LuBP4vIWhEZJiJXW9exTkQWNugP3gCllPly8S8gBj0qM97a/gK46STHLgeusF57ox/XvxKYi54bpBV6OHlrdO3gsPXaC9gH/N1674PAy9brD4HZ6P/QOqOf7/EG/gK8bx3T1TqvN3ALesRsoLW9G4hCLwS2EPC13vMY8DfrdSpwv/X6XuA96/Vk4JEq17cBaGu9DrL738bVv0wNpvnYpZRaa71ehU461YiIP/qPbwaAUqpQKXUUGAp8ppQqU0odBBYA/ay3rVR6bpwiYAdQ/mj/hj98xhdKKadSKgWdPLpa5/3Y+qyt6EQSax3/q1IqVylViH72px16Yq/uwGLr8YzxVnm58gdOT3h9lsXAhyJyJzphGg3IPIvUfBRVeV0GnLCJVMfzOqtsO6n++/XHZ1JO94zKH+N1BwSYq5S6/jTvKT/+OEqpu0VkAHrSrFUi0lcplX2aWIwzZGowRgWlZ+ZLE5HLAUTES0R8gEXAtdZcvOHoGd5W1PL0V4uIm9Uv0wHYZp33RuuzYoFoq/xklgFDRKST9R5f632nkgf4l2+ISEel1HKl1N/QE0lF1fI6jFowCcb4o3HAAyKyHlgCRAAzgPXAOmAe8KjS0xjUxh50UvoJuNtq+rwJuInIBmA6cIvV1DohpVQmun/mMyu+peim1qn8AFxR3skLvGB1Am+0rm9dLa/DqAXzNLXR4ETkQ+BHpdRXdsdiNC5TgzEMo8GYGkwzJSJvoCfNquoVpdQHdsRjuCaTYAzDaDCmiWQYRoMxCcYwjAZjEoxhGA3GJBjDMBqMSTCGYTSY/w8Az0awv03rxwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "results = []\n",
    "covariance_types = ['full', 'tied', 'diag', 'spherical']\n",
    "for n_components in range(1, 9):\n",
    "    for covariance_type in covariance_types:\n",
    "        mclust = GaussianMixture(n_components = n_components, warm_start=True,\n",
    "                                 covariance_type = covariance_type)\n",
    "        mclust.fit(df)\n",
    "        results.append({\n",
    "            'bic': mclust.bic(df),\n",
    "            'n_components': n_components,\n",
    "            'covariance_type': covariance_type,\n",
    "        })\n",
    "        \n",
    "results = pd.DataFrame(results)\n",
    "\n",
    "colors = ['C0', 'C1', 'C2', 'C3']\n",
    "styles = ['C0-','C1:','C0-.', 'C1--']\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(4, 4))\n",
    "for i, covariance_type in enumerate(covariance_types):\n",
    "    subset = results.loc[results.covariance_type == covariance_type, :]\n",
    "    subset.plot(x='n_components', y='bic', ax=ax, label=covariance_type, \n",
    "                kind='line', style=styles[i]) # , color=colors[i])\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Scaling and Categorical Variables\n",
    "## Scaling the Variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      loan_amnt     annual_inc     revol_bal   open_acc        dti  \\\n",
      "0  10637.693847   42631.523547  10320.622383   9.598871  17.704792   \n",
      "1  22001.268591  167220.697288  39261.439195  12.593176  13.378101   \n",
      "2  18318.495256   83980.990779  19769.353601  11.677669  16.766443   \n",
      "3  22570.192308  489783.403846  85161.346154  13.326923   6.907500   \n",
      "\n",
      "   revol_util   size  \n",
      "0   58.148316  13974  \n",
      "1   63.351943   1147  \n",
      "2   62.310556   7498  \n",
      "3   59.651923     52  \n"
     ]
    }
   ],
   "source": [
    "loan_data = pd.read_csv(LOAN_DATA_CSV)\n",
    "loan_data['outcome'] = pd.Categorical(loan_data['outcome'], \n",
    "                                      categories=['paid off', 'default'], \n",
    "                                      ordered=True)\n",
    "defaults = loan_data.loc[loan_data['outcome'] == 'default',]\n",
    "\n",
    "columns = ['loan_amnt', 'annual_inc', 'revol_bal', 'open_acc', \n",
    "           'dti', 'revol_util']\n",
    "\n",
    "df = defaults[columns]\n",
    "kmeans = KMeans(n_clusters=4, random_state=1).fit(df)\n",
    "counts = Counter(kmeans.labels_)\n",
    "\n",
    "centers = pd.DataFrame(kmeans.cluster_centers_, columns=columns)\n",
    "centers['size'] = [counts[i] for i in range(4)]\n",
    "print(centers)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      loan_amnt     annual_inc     revol_bal   open_acc        dti  \\\n",
      "0  13466.944801   55898.294929  16405.578306  14.325738  24.202701   \n",
      "1  10501.878203   51108.842190  11640.525627   7.508902  15.946078   \n",
      "2  10319.056956   53440.614753   6044.048926   8.657516  11.285520   \n",
      "3  25941.737057  116654.232970  32900.941144  12.391826  16.176403   \n",
      "\n",
      "   revol_util  size  \n",
      "0   59.387697  6240  \n",
      "1   77.786191  7401  \n",
      "2   30.987120  5345  \n",
      "3   66.132281  3685  \n"
     ]
    }
   ],
   "source": [
    "scaler = preprocessing.StandardScaler()\n",
    "df0 = scaler.fit_transform(df * 1.0)\n",
    "\n",
    "kmeans = KMeans(n_clusters=4, random_state=1).fit(df0)\n",
    "counts = Counter(kmeans.labels_)\n",
    "\n",
    "centers = pd.DataFrame(scaler.inverse_transform(kmeans.cluster_centers_), \n",
    "                       columns=columns)\n",
    "centers['size'] = [counts[i] for i in range(4)]\n",
    "print(centers)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dominant Variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "syms = ['GOOGL', 'AMZN', 'AAPL', 'MSFT', 'CSCO', 'INTC', 'CVX', 'XOM', \n",
    "        'SLB', 'COP', 'JPM', 'WFC', 'USB', 'AXP', 'WMT', 'TGT', 'HD', 'COST']\n",
    "top_sp1 = sp500_px.loc[sp500_px.index >= '2005-01-01', syms]\n",
    "\n",
    "sp_pca1 = PCA()\n",
    "sp_pca1.fit(top_sp1)\n",
    "\n",
    "explained_variance = pd.DataFrame(sp_pca1.explained_variance_)\n",
    "ax = explained_variance.head(10).plot.bar(legend=False, figsize=(4, 4))\n",
    "ax.set_xlabel('Component')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              0         1\n",
      "GOOGL -0.857310  0.477873\n",
      "AMZN  -0.444728 -0.874149\n",
      "AAPL  -0.071627 -0.020802\n",
      "MSFT  -0.036002 -0.006204\n",
      "CSCO  -0.029205 -0.003045\n",
      "INTC  -0.026666 -0.006069\n",
      "CVX   -0.089548 -0.037420\n",
      "XOM   -0.080336 -0.020511\n",
      "SLB   -0.110218 -0.030356\n",
      "COP   -0.057739 -0.024117\n",
      "JPM   -0.071228 -0.009244\n",
      "WFC   -0.053228 -0.008597\n",
      "USB   -0.041670 -0.005952\n",
      "AXP   -0.078907 -0.024027\n",
      "WMT   -0.040346 -0.007141\n",
      "TGT   -0.063659 -0.024662\n",
      "HD    -0.051412 -0.032922\n",
      "COST  -0.071403 -0.033826\n"
     ]
    }
   ],
   "source": [
    "loadings = pd.DataFrame(sp_pca1.components_[0:2, :], \n",
    "                        columns=top_sp1.columns)\n",
    "print(loadings.transpose())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Categorical Data and Gower's Distance\n",
    "> Currently not available in any of the standard packages. However work is in progress to add it to scikit-learn. We will update this notebook once it becomes available\n",
    "\n",
    "https://github.com/scikit-learn/scikit-learn/pull/9555/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     dti  payment_inc_ratio home_            purpose_\n",
      "0   1.00            2.39320  RENT      major_purchase\n",
      "1   5.55            4.57170   OWN      small_business\n",
      "2  18.08            9.71600  RENT               other\n",
      "3  10.08           12.21520  RENT  debt_consolidation\n",
      "4   7.06            3.90888  RENT               other\n"
     ]
    }
   ],
   "source": [
    "x = defaults[['dti', 'payment_inc_ratio', 'home_', 'purpose_']].loc[0:4, :]\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```\n",
    "\n",
    "###############################################################\n",
    "## Figure 7-13: Categorical data and Gower's distance\n",
    "\n",
    "x <- loan_data[1:5, c('dti', 'payment_inc_ratio', 'home_', 'purpose_')]\n",
    "x\n",
    "\n",
    "daisy(x, metric='gower')\n",
    "\n",
    "set.seed(301)\n",
    "df <- loan_data[sample(nrow(loan_data), 250),\n",
    "                c('dti', 'payment_inc_ratio', 'home_', 'purpose_')]\n",
    "d = daisy(df, metric='gower')\n",
    "hcl <- hclust(d)\n",
    "dnd <- as.dendrogram(hcl)\n",
    "\n",
    "png(filename=file.path(PSDS_PATH, 'figures', 'psds_0713.png'), width = 4, height=4, units='in', res=300)\n",
    "par(mar=c(0,5,0,0)+.1)\n",
    "plot(dnd, leaflab='none', ylab='distance')\n",
    "dev.off()\n",
    "\n",
    "dnd_cut <- cut(dnd, h=.5)\n",
    "df[labels(dnd_cut$lower[[1]]),]\n",
    "\n",
    "\n",
    "## Problems in clustering with mixed data types\n",
    "df <- model.matrix(~ -1 + dti + payment_inc_ratio + home_ + pub_rec_zero, data=defaults)\n",
    "df0 <- scale(df)\n",
    "km0 <- kmeans(df0, centers=4, nstart=10)\n",
    "centers0 <- scale(km0$centers, center=FALSE, scale=1/attr(df0, 'scaled:scale'))\n",
    "round(scale(centers0, center=-attr(df0, 'scaled:center'), scale=FALSE), 2)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problems with Clustering Mixed Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         dti  payment_inc_ratio  pub_rec_zero  home__MORTGAGE     home__OWN  \\\n",
      "0  17.456244           8.422914  1.000000e+00    1.000000e+00 -6.938894e-17   \n",
      "1  16.992128           9.105395  1.000000e+00   -1.110223e-16 -3.330669e-16   \n",
      "2  17.197993           9.266666  9.179025e-01    9.436896e-16  1.000000e+00   \n",
      "3  16.504955           8.064247 -4.440892e-16    5.156600e-01 -1.804112e-16   \n",
      "\n",
      "     home__RENT  \n",
      "0 -3.108624e-15  \n",
      "1  1.000000e+00  \n",
      "2 -6.661338e-16  \n",
      "3  4.843400e-01  \n"
     ]
    }
   ],
   "source": [
    "columns = ['dti', 'payment_inc_ratio', 'home_', 'pub_rec_zero']\n",
    "df = pd.get_dummies(defaults[columns])\n",
    "\n",
    "scaler = preprocessing.StandardScaler()\n",
    "\n",
    "df0 = scaler.fit_transform(df * 1.0)\n",
    "kmeans = KMeans(n_clusters=4, random_state=1).fit(df0)\n",
    "centers = pd.DataFrame(scaler.inverse_transform(kmeans.cluster_centers_), \n",
    "                       columns=df.columns)\n",
    "print(centers)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
